Finite Group Databasebeta

← #14437711

Subgroups — #14437711

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×C4⋊Q8C211yesmaximal, characteristic
2#11752562C211yesmaximal, characteristic
3C5×#5079C211yesmaximal, characteristic, complemented
4C3×#65370C211yesmaximal, characteristic, complemented
5#11749203C214yesmaximal
6#11749189C214yesmaximal, complemented
7C4×#6648C211yesmaximal, characteristic
8#11746930C211yesmaximal, characteristic, complemented
9#11746921C211yesmaximal, characteristic, complemented
10D5×#487—31nomaximal, Hall
11C2×Q8×D15C2212yes—
12C2×D15⋊Q8—21no—
13C3×C5×C4⋊Q8C2211yescharacteristic
14#91833C2212yes—
15C4⋊C4×D15—21no—
16C4⋊C4×D15—21no—
17#91777—21no—
18#91777—21no—
19C42×D15C2211yescharacteristic
20#91758C2211yescharacteristic
21C5×#869C2211yescharacteristic
22C3×#4015C2211yescharacteristic
23#91470—21no—
24#91470C2212yes—
25#91437—21no—
26#91437C2212yes—
27#91385—21no—
28C2×#6648C2212yes—
29C5×#835C2214yes—
30C4×C5×C3⋊C8C2211yescharacteristic
31C3×#3967C2214yes—
32C3×C4×#168C2211yescharacteristic
33#90975C2214yes—
34#90974C2214yes—
35#90951C2212yes—
36D3×#487—51nomaximal, Hall
37D5×C4⋊Q8—31no—
38D5×C4⋊Q8—31no—
39C5×#487—31no—
40#65382—31no—
41#65370D311yescharacteristic, complemented
42D5×#103—34no—
43#65081—34no—
44C4×C8×D5—31no—
45#64970—31no—
46C2×C3×C5×Q8C2312yes—
47Q8×D15—28no—
48C2×C4×D15—22no—
49C2×C4×D15D411yescharacteristic
50C2×C4×D15D411yescharacteristic
51C2×C4×D15C2311yescharacteristic
52C2×Dic30—22no—
53C2×Dic30C2312yes—
54C2×C5×Dic6—21no—
55C2×C3×Dic10—21no—
56C2×#1204—22no—
57C2×#1200—22no—
58D15⋊Q8—44no—
59C3×C5×C4⋊C4—21no—
60C3×C5×C4⋊C4—21no—
61C3×C42×C5C2311yescharacteristic
62C4⋊Dic15—21no—
63C4⋊Dic15—21no—
64#6712—22no—
65#6712—22no—
66C4×Dic15D411yescharacteristic
67C4×Dic15D411yescharacteristic
68C4×Dic15C2311yescharacteristic
69C5×C4⋊Dic3—21no—
70C5×C4⋊Dic3C2312yes—
71C2×C5×C3⋊C8C2312yes—
72C3×C4⋊Dic5—21no—
73C3×C4⋊Dic5C2312yes—
74C2×C3×#168C2312yes—
75#6669—22no—
76#6669—22no—
77#6648—24no—
78D3×C4⋊Q8—51no—
79D3×C4⋊Q8—51no—
80C3×#487—51no—
81#5093—51no—
82#5079D511yescharacteristic, complemented
83D3×#103—54no—
84#4792—54no—
85C4×D3×C8—51no—
86#4681—51no—
87C2×Q8×D5—32no—
88C2×Q8×D5—61no—
89C5×C4⋊Q8—31no—
90C5×C4⋊Q8C2×D311yescharacteristic
91#4090—32no—
92#4090—61no—
93C2×C8×D5—32no—
94D5×C4⋊C4—32no—
95D5×C4⋊C4—61no—
96D5×C4⋊C4—61no—
97D5×C4⋊C4—61no—
98#4034—32no—
99#4034—61no—
100#4034—61no—
101#4034—61no—
102C42×D5—31no—
103#4015—31no—
104#4015C2×D311yescharacteristic
105C5×#103—34no—
106C4×C5×C8—31no—
107#3967C2×D314yes—
108#3948—34no—
109C8×Dic5—32no—
110#3942—34no—
111C4×#168C2×D311yescharacteristic
112C2×#487—151noSylow
113C22×D15C2×D411yescharacteristic
114C3×C5×Q8—24no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2411yescharacteristic
119C2×Dic15—22no—
120C2×Dic15C2×D411yescharacteristic
121C2×Dic15C2×D411yescharacteristic
122C2×Dic15C2×D411yescharacteristic
123C4×D15—44no—
124C4×D15SD1614yes—
125C4×D15Q1614yes—
126C4×D15#4114yes—
127Dic30—24no—
128Dic30—44no—
129C2×C5×Dic3—22no—
130C5×Dic6—42no—
131C2×C3×Dic5—22no—
132C3×Dic10—42no—
133#1204—44no—
134#1200—44no—
135C3×#168—22no—
136C5×C3⋊C8—22no—
137C2×D3×Q8—52no—
138C2×D3×Q8—101no—
139C3×C4⋊Q8—51no—
140C3×C4⋊Q8C2×D511yescharacteristic
141#944—52no—
142#944—101no—
143C2×D3×C8—52no—
144D3×C4⋊C4—52no—
145D3×C4⋊C4—101no—
146D3×C4⋊C4—101no—
147D3×C4⋊C4—101no—
148#888—52no—
149#888—101no—
150#888—101no—
151#888—101no—
152C42×D3—51no—
153#869—51no—
154#869C2×D511yescharacteristic
155C3×#103—54no—
156C3×C4×C8—51no—
157#835C2×D514yes—
158#816—54no—
159C8×Dic3—52no—
160#810—54no—
161C4×C3⋊C8C2×D511yescharacteristic
162C2×C5×Q8—61no—
163C2×C5×Q8C22×D312yes—
164Q8×D5—68no—
165Q8×D5—124no—
166C2×C4×D5—31no—
167C2×C4×D5—31no—
168C2×C4×D5—31no—
169C2×C4×D5—62no—
170C2×C4×D5—62no—
171C2×Dic10—21no—
172C2×Dic10—32no—
173C2×Dic10—62no—
174C2×Dic10—62no—
175C2×C5×C8—32no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—32no—
179C5×C4⋊C4—61no—
180C42×C5C22×D311yescharacteristic
181C4⋊Dic5—21no—
182C4⋊Dic5—61no—
183C4⋊Dic5—61no—
184C4⋊Dic5C22×D312yes—
185#683—62no—
186#683—62no—
187#683—62no—
188#683—62no—
189C4×Dic5—31no—
190C4×Dic5—31no—
191C4×Dic5—31no—
192C2×#168C22×D312yes—
193C8×D5—64no—
194C2×C4⋊Q8—151no—
195C2×C4⋊Q8—151no—
196#487—31no—
197#487—51no—
198#487—151no—
199#487—151no—
200#487—154no—
201C2×#103—154no—
202C2×C4×C8—151no—
203C22×C3×C5C22×D411yescharacteristic
204C2×D15#12412yes—
205C2×D15C2×SD1612yes—
206C2×D15C2×Q1612yes—
207C3×C4×C5—42no—
208C3×C4×C5C2×SD1612yes—
209C3×C4×C5C2×Q1612yes—
210C3×C4×C5C2×#4112yes—
211Dic15—42no—
212Dic15#12412yes—
213Dic15C2×SD1612yes—
214Dic15C2×Q1612yes—
215C3×Dic5—42no—
216C5×Dic3—42no—
217C2×C3×Q8—101no—
218C2×C3×Q8C22×D512yes—
219D3×Q8—108no—
220D3×Q8—204no—
221C2×C4×D3—51no—
222C2×C4×D3—51no—
223C2×C4×D3—51no—
224C2×C4×D3—102no—
225C2×C4×D3—102no—
226C2×Dic6—21no—
227C2×Dic6—52no—
228C2×Dic6—102no—
229C2×Dic6—102no—
230C2×C3×C8—52no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—52no—
234C3×C4⋊C4—101no—
235C3×C42C22×D511yescharacteristic
236C4⋊Dic3—21no—
237C4⋊Dic3—101no—
238C4⋊Dic3—101no—
239C4⋊Dic3C22×D512yes—
240Dic3⋊C4—102no—
241Dic3⋊C4—102no—
242Dic3⋊C4—102no—
243Dic3⋊C4—102no—
244C4×Dic3—51no—
245C4×Dic3—51no—
246C4×Dic3—51no—
247C2×C3⋊C8C22×D512yes—
248D3×C8—104no—
249C22×D5—31no—
250C5×Q8—24no—
251C5×Q8—122no—
252C2×C4×C5—22no—
253C2×C4×C5—62no—
254C2×C4×C5D3×D411yescharacteristic
255C2×C4×C5D3×D411yescharacteristic
256C2×C4×C5C23×D311yescharacteristic
257C2×Dic5—22no—
258C2×Dic5—31no—
259C2×Dic5—31no—
260C2×Dic5—31no—
261C2×Dic5—62no—
262C4×D5—34no—
263C4×D5—34no—
264C4×D5—34no—
265C4×D5—124no—
266C4×D5—124no—
267Dic10—42no—
268Dic10—64no—
269Dic10—124no—
270Dic10—124no—
271C5×C8—62no—
272#168—22no—
273C22×Q8—152no—
274C22×Q8—301no—
275C22×C8—152no—
276C4⋊Q8—31no—
277C4⋊Q8—51no—
278C4⋊Q8—152no—
279C4⋊Q8—152no—
280C4⋊Q8—151no—
281C4⋊Q8—301no—
282C4⋊Q8—301no—
283C4⋊Q8—301no—
284C4⋊Q8—301no—
285C4⋊Q8D3×D511yescharacteristic
286C2×C4⋊C4—152no—
287C2×C4⋊C4—301no—
288C2×C4⋊C4—301no—
289C2×C4⋊C4—301no—
290C2×C42—151no—
291#103—34no—
292#103—54no—
293#103—154no—
294#103—154no—
295C4×C8—31no—
296C4×C8—51no—
297C4×C8—152no—
298C2×C3×C5C2×#12411yescharacteristic
299C2×C3×C5C22×SD1611yescharacteristic
300C2×C3×C5C22×Q1611yescharacteristic
301D15#48714yescomplemented
302C22×D3—51no—
303C3×Q8—24no—
304C3×Q8—202no—
305C2×C3×C4—22no—
306C2×C3×C4—102no—
307C2×C3×C4D4×D511yescharacteristic
308C2×C3×C4D4×D511yescharacteristic
309C2×C3×C4C23×D511yescharacteristic
310C2×Dic3—22no—
311C2×Dic3—51no—
312C2×Dic3—51no—
313C2×Dic3—51no—
314C2×Dic3—102no—
315C4×D3—54no—
316C4×D3—54no—
317C4×D3—54no—
318C4×D3—204no—
319C4×D3—204no—
320Dic6—42no—
321Dic6—104no—
322Dic6—204no—
323Dic6—204no—
324C3×C8—102no—
325C3⋊C8—22no—
326C22×C5C2×D3×D411yescharacteristic
327C2×D5—32no—
328C2×D5—32no—
329C2×D5—32no—
330C4×C5—42no—
331C4×C5—122no—
332C4×C5D3×SD1612yes—
333C4×C5D3×Q1612yes—
334C4×C5D3×#4112yes—
335Dic5—32no—
336Dic5—32no—
337Dic5—32no—
338Dic5—42no—
339Dic5—122no—
340C2×Q8—61no—
341C2×Q8—101no—
342C2×Q8—152no—
343C2×Q8—302no—
344C2×Q8—302no—
345C2×Q8—308no—
346C2×Q8—604no—
347C2×Q8C2×D3×D512yes—
348C22×C4—151no—
349C22×C4—151no—
350C22×C4—151no—
351C22×C4—302no—
352C22×C4—302no—
353C2×C8—32no—
354C2×C8—52no—
355C2×C8—304no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—32no—
359C4⋊C4—52no—
360C4⋊C4—61no—
361C4⋊C4—101no—
362C4⋊C4—302no—
363C4⋊C4—302no—
364C4⋊C4—302no—
365C4⋊C4—302no—
366C4⋊C4—301no—
367C4⋊C4—301no—
368C42—151no—
369C42—151no—
370C42—151no—
371C42C2×D3×D511yescharacteristic
372C3×C5C2×#48711yescharacteristic, complemented, Hall
373C22×C3C2×D4×D511yescharacteristic
374C2×D3—52no—
375C2×D3—52no—
376C2×D3—52no—
377C3×C4—42no—
378C3×C4—202no—
379C3×C4D5×SD1612yes—
380C3×C4D5×Q1612yes—
381C3×C4D5×#4112yes—
382Dic3—42no—
383Dic3—52no—
384Dic3—52no—
385Dic3—52no—
386Dic3—202no—
387C2×C5D3×#12411yescharacteristic
388C2×C5C2×D3×SD1611yescharacteristic
389C2×C5C2×D3×Q1611yescharacteristic
390D5—34no—
391C23—151no—
392Q8—24no—
393Q8—122no—
394Q8—202no—
395Q8—304no—
396Q8—604no—
397Q8—604no—
398C2×C4—22no—
399C2×C4—62no—
400C2×C4—102no—
401C2×C4—151no—
402C2×C4—151no—
403C2×C4—151no—
404C2×C4—154no—
405C2×C4—154no—
406C2×C4—154no—
407C2×C4—302no—
408C2×C4—604no—
409C2×C4—604no—
410C2×C4#679011yescharacteristic
411C2×C4#679011yescharacteristic
412C2×C4C22×D3×D511yescharacteristic
413C8—62no—
414C8—102no—
415C2×C3D5×#12411yescharacteristic
416C2×C3C2×D5×SD1611yescharacteristic
417C2×C3C2×D5×Q1611yescharacteristic
418D3—54no—
419C5D3×#48711yescharacteristic, complemented, Sylow
420C22—152no—
421C22—152no—
422C22—152no—
423C22C2×#679011yescharacteristic
424C4—42no—
425C4—122no—
426C4—152no—
427C4—152no—
428C4—152no—
429C4—202no—
430C4—602no—
431C4#9150512yes—
432C4#9151112yes—
433C4#9202412yes—
434C3D5×#48711yescharacteristic, complemented, Sylow
435C2—154no—
436C2#1175483111yescharacteristic
437C2C2×#9150511yescharacteristic
438C2C2×#9151111yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5C2×#487
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C5×#5079C2semidirect
4. C3×#65370C2semidirect
6. #11749189C2semidirect
8. #11746930C2semidirect
9. #11746921C2semidirect
41. #65370D3semidirect
82. #5079D5semidirect
301. D15#487semidirect
372. C3×C5C2×#487semidirect
419. C5D3×#487semidirect
434. C3D5×#487semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D15×C4⋊Q82
#117525622
C5×#50792
C3×#653702
#117492032
#117491892
C4×#66482
#117469302
#117469212
D5×#4873
D3×#4875